Not sure on this one Bro, but in time past ! an auto licence only allowed to to dive autos, a manual licence covered both, so ask the DVLA they'll be more likely know, or not given it's their department!
Best to up date your licence
If it only has two peddles it is auto, regardless id it is called DSG, DCT, Flappy paddle, tiptronic or whatever. They are all classed as Automatic.
Paddle changes are more or less equivalent to the old pre-selector boxes that some vehicles used to have. "Semi-automatic" isn't really a meaningful term for these. The only thing that's automated is the clutch. The driver still has to do the gear changes, these just have an electronic selector mechanism instead of a manual lever and linkage.
They are not automatic because the system requires driver input whilst the car is moving; so you need a "manual" licence.
As far as I understand it, whether or not you can drive a car with an auto licence depends on whether there's a clutch pedal or not. If it's got a clutch it's a manual and you need a manual licence, if it's any type of semi auto or flappy paddle thing it's counted as an auto.
Bear in mind even in an old style slushbox type auto with the PRND selector, you could still manually select the lower gears so that alone doesn't qualify it as a manual car.